Binary fractions of G and K dwarf stars based on the Gaia EDR3 and LAMOST DR5: impacts of the chemical abundances

Basing on the large volume \textit{Gaia} Early Data Release 3 and LAMOST Data Release 5 data, we estimate the bias-corrected binary fractions of the field late G and early K dwarfs. A stellar locus outlier method is used in this work, which works well for binaries of various periods and inclination angles with single epoch data. With a well-selected, distance-limited sample of about 90 thousand GK dwarfs covering wide stellar chemical abundances, it enables us to explore the binary fraction variations with different stellar populations. The average binary fraction is 0.42$\pm$0.01 for the whole sample. Thin disk stars are found to have a binary fraction of 0.39$\pm$0.02, thick disk stars own a higher one of 0.49$\pm$0.02, while inner halo stars possibly own the highest binary fraction. For both the thin and thick disk stars, the binary fractions decrease toward higher [Fe/H], [$\alpha$/H], and [M/H] abundances. However, the suppressing impacts of the [Fe/H], [$\alpha$/H], and [M/H] are more significant for the thin disk stars than those for the thick disk stars. For a given [Fe/H], a positive correlation between [$\alpha$/Fe] and the binary fraction is found for the thin disk stars. However, this tendency disappears for the thick disk stars. We suspect that it is likely related to the different formation histories of the thin and thick disks. Our results provide new clues for theoretical works on binary formation.